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arXiv · 2201.05505

Parabolic frequency on Ricci flows

Julius Baldauf·Dain Kim
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Abstract

This paper defines a parabolic frequency for solutions of the heat equation on a Ricci flow and proves it's monotonicity along the flow. Frequency monotonicity is known to have many useful consequences; here it is shown to provide a simple proof of backwards uniqueness. For solutions of more general parabolic equations on a Ricci flow, this paper provides bounds on the derivative of the frequency, which similarly imply backwards uniqueness.

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Julius Baldauf, Dain Kim. 2022-01-14. Parabolic frequency on Ricci flows. https://arxiv.org/abs/2201.05505

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